Whereas the positive equilibrium of a mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.
@article{arxiv.2103.00972,
title = {Oscillations in planar deficiency-one mass-action systems},
author = {Balázs Boros and Josef Hofbauer},
journal= {arXiv preprint arXiv:2103.00972},
year = {2024}
}